
\documentclass[tikz,border=10pt]{standalone}


\RequirePackage{luatex85}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb, amsfonts, accents}
\usetikzlibrary{graphdrawing, graphs, shapes, arrows}
\usegdlibrary{trees}
\usepackage{stix}

\newcommand{\IRE}{I\!RE}

\begin{document}

%\begin{tikzpicture}[>=stealth, every node/.style={rectangle, rounded corners, draw, minimum size=0.1in}]
\begin{tikzpicture}[>=stealth, every node/.style={draw=none, minimum size=0.1}]

\begin{scope}[xshift=2.5in]
%    \node [rectangle, rounded corners, draw, minimum width=3.7in, minimum height=1.9in, yshift=-0.7in] {};
%    \node[yshift=0.3in, draw=none] {$t_1: T(T(\varnothing, T(a)), T(\varnothing))$};
    \graph [tree layout, grow=down, fresh nodes] {
        "${(1, 1, \cdot)}_{\Lambda}$" -- {
            "${(2, 2, |)}_{1}$" -- {
                "${(0, 0, \epsilon)}_{1.1}$"[draw=none],
                "${(0, 0, \{0,\infty\})}_{1.2}$"[draw=none] -- {
                    "${(0, 0, a)}_{1.2.1}$"[draw=none]
                }
            },
            "${(3, 0, \{0,\infty\})}_{2}$" -- {
                "${(4, 3, |)}_{2.1}$" -- {
                    "${(0, 0, a)}_{2.1.1}$"[draw=none],
                    "${(0, 0, \epsilon)}_{2.1.2}$"[draw=none]
                }
            }
        }
    };
    \node[xshift=0in, yshift=-1.5in, draw=none]
    {\small{$
    \IRE ((\epsilon|a^{0,\infty})(\epsilon|a)^{0,\infty} )) = (1,1,(2,2,(0,0,\epsilon) \mid (0,0,(0,0,a)^{0,\infty}))
        \cdot (3,0,(4,3,(0,0,\epsilon) \mid (0,0,a))^{0,\infty}))
    $}};
%    \node[xshift=0in, yshift=-1.7in, draw=none] {$(\epsilon | a^{0,\infty})(a | \epsilon)^{0,\infty}$};
\end{scope}

\begin{scope}[xshift=0in, yshift=-2in]
    \node[xshift=-0.3in, draw=none] {$s:$};
    \graph [tree layout, grow=down, fresh nodes] {
        "${T}^{1}_{\Lambda}$" -- {
            "${T}^{2}_{1}$" -- {
                "${\varnothing}^{0}_{1.1}$"[draw=none],
                "${T}^{0}_{1.2}$"[draw=none] -- {
                    "${a}^{0}_{1.2.1}$"[draw=none]
                }
            },
            "${T}^{3}_{2}$" -- {
                "${\varnothing}^{4}_{2.1}$"
            }
        }
    };
    \node[yshift=-1.5in, draw=none]
    {\small{${T}^{1} \big(
        {T}^{2} \big(
            {\varnothing}^{0},
            {T}^{0}({a}^{0})
        \big),
        {T}^{3}(
            {\varnothing}^{4}
        )
    \big)$}};
\end{scope}

\begin{scope}[xshift=2in, yshift=-2in]
    \node[xshift=-0.3in, draw=none] {$t:$};
    \graph [tree layout, grow=down, fresh nodes] {
        "${T}^{1}_{\Lambda}$" -- {
            "${T}^{2}_{1}$" -- {
                "${\varnothing}^{0}_{1.1}$"[draw=none],
                "${T}^{0}_{1.2}$"[draw=none] -- {
                    "${\varnothing}^{0}_{1.2.1}$"[draw=none]
                }
            },
            "${T}^{3}_{2}$" -- {
                "${T}^{4}_{2.1}$" -- {
                    "${a}^{0}_{2.1.1}$"[draw=none],
                    "${\varnothing}^{0}_{2.1.2}$"[draw=none]
                }
            }
        }
    };
    \node[yshift=-1.5in, draw=none]
    {\small{${T}^{1}\big(
        {T}^{2}(
            {\varnothing}^{0},
            {T}^{0}({\varnothing}^{0})
        ),
        {T}^{3}\big(
            {T}^{4}({a}^{0},{\varnothing}^{0})
        \big)
    \big)$}};
\end{scope}

\begin{scope}[xshift=4.2in, yshift=-2in]
    \node[xshift=-0.3in, draw=none] {$u:$};
    \graph [tree layout, grow=down, fresh nodes] {
        "${T}^{1}_{\Lambda}$" -- {
            "${T}^{2}_{1}$" -- {
                "${\epsilon}^{0}_{1.1}$"[draw=none],
                "${\varnothing}^{0}_{1.2}$"[draw=none]
            },
            "${T}^{3}_{2}$" -- {
                "${T}^{4}_{2.1}$" -- {
                    "${a}^{0}_{2.1.1}$"[draw=none],
                    "${\varnothing}^{0}_{2.1.2}$"[draw=none]
                },
                "${T}^{4}_{2.2}$" -- {
                    "${\varnothing}^{0}_{2.2.1}$"[draw=none],
                    "${\epsilon}^{0}_{2.2.2}$"[draw=none]
                }
            }
        }
    };
    \node[xshift=0.2in, yshift=-1.5in, draw=none]
    {\small{${T}^{1}\big(
        {T}^{2}(
            {\epsilon}^{0},
            {\varnothing}^{0}
        ),
        {T}^{3}\big(
            {T}^{4}({a}^{0},{\varnothing}^{0}),
            {T}^{4}({\varnothing}^{0}, {\epsilon}^{0})
        \big)
    \big)$}};
\end{scope}

\end{tikzpicture}

\end{document}

